(2) Ask or Answer a question related to our recent class content on the wiki page.

(3) Nelson 5.5

(4) You have two microcentrifuge tubes (a cylinder R=0.5cm, L=3cm), one with a solution of bacteria (R=1 micron) and one with a solution of eukaryotic cells (R=10 micron). You want to exchange the buffer they are in, so you want to force all cells to a small pellet at the bottom of the tube using a centrifuge. You also don't want it to take more than 5 minutes. If the centrifuge radius is 10 cm, how fast do you have to spin? What is the acceleration in g?

(3) Imagine you are building a pH sensor based on a molecule that weakly binds H. The molecule with a bound H has a different Raman scattering signature than the unbound molecule. Each "sensor" is a 100 nm bead with 1000 such molecules. If 50% of molecules are occupied at pH 6, show (a) the percent occupied vs pH, (b) the sensitivity vs pH given by dS/d(pH) where S=Nunbound/(Nunbound + Nbound).

(4) Numerical warmup: Compute numerically a 30 second trajectory of a membrane protein diffusing with D=0.05 micron^2/s. Use 1000 time steps to generate the trajectory. Use the computer program of your choice (but MATLAB is recommended). Give the code, and the trajectory with properly labeled axes.

(2) Compare the force extension curves of simulated Worm Like Chains (WLCs) to the approximate functional form given by Nelson eq. 9.42. Assume a link size of 1 nm, persistence length of 50 nm and that the applied force is along the z axis.

(a) Given a link with direction r(θ,φ), where θ is polar angle from the z-axis, find the probability of the next link r'(θ,φ,θ',φ').

(b) Show how to make a random selection of θ',φ' from the probability distribution in (a) when given random numbers uniformly distributed from 0 to 1.

(c) Use (a) and (b) to construct a 1000 link chain for a certain force.

(d) Repeat (c) as many times as necessary for the same force to obtain a well defined <z>.

(e) Repeat (d) for several different forces between 0 and the force that gives <z>~Lo where Lo is the T=0 K length.

(f) Plot <z> vs f of your simulation with errors given by standard error of the mean. On the same plot also show eq. 9.42. Be sure to include correct units.